Does anyone have any insight as to how I could draw a spiral spring (like these http://www.google.com/images?q=spiral+spring) unwinding?

I have discovered how to draw an Archimedean spiral (http://www.pixelwit.com/blog/2008/04...draw-a-spiral/) and a Logarithmic spiral (http://www.pixelwit.com/blog/2008/05...ithmic-spiral/), but this is a bit more complex. The constant is the length of the spring, and the tighter it is wound, the more loops. I tried using a rotating radius, rotating it more degrees and shortening it as I drew depending on the tightness, but that doesn't quite work. Any ideas would be much appreciated.